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If is a positive integer write an integral to represent .

Notice that this is a Riemann sum with infinitely many rectangles.

And a Riemann sum with infinitely many rectangles is the Definition of an Integral:

Can you rewrite this as an integral?

The represents the infinitely small width of each rectangle.
Now lets find the height of each rectangle.
Heights, of course, are represented by a function, .
But what is ?

Since is a variable, we will let represent the part of the series that is changing:

We still need to find the bounds of the integral.